APMA 0350

Welcome to APMA 0350, an exciting dif-fun-rential equations adventure awaits you! On this website, you can find the syllabus, lecture notes, homework assignments, and study materials.

Syllabus

APMA 0350 – Syllabus

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Lecture Notes

Note: The lecture notes will be frequently updated. Please refresh your webpage so that you have the most up-to-date version of the notes.

#	Date	Lecture Notes	Lecture Videos
1	Sep 3	What is a differential equation?	What is a differential equation?
			Basic ODE
			Solutions of ODE
			Existence and uniqueness
2	Sep 5	Direction Fields	Classification of ODE
			Direction fields
			dfield app
			Pretty pictures
3	Sep 8	Qualitative Methods	Autonomous ODE
			Logistic Equation
			More Qualitative Study
4	Sep 10	Existence and Uniqueness	Existence and Uniqueness
			ODE with a Twist
			Dangerous ODE
			Existence Uniqueness Theorem
5	Sep 12	Separation of Variables	Motivation
			Separation of Variables
			Implicit Solutions
			Logistic Equation
			Hidden Solutions
			Why this works
6	Sep 15	Integrating Factors	Motivation
			Integrating Factors: Simple
			Integrating Factors Example
			Integrating Factors: General
			Why this works
			Integrating Factors Practice
7	Sep 17	Applications	Falling Object
			To the Moon
			More to the Moon
			Compartmental Models
			Chemical Tanks
8	Sep 19	Exact Equations	Exact Equations
			Multivariable Review
			Solving Exact ODE
			Exact ODE Practice
			Nonexact equations
			Why this works
9	Sep 22	Euler’s Method (I)	Euler’s Method Motivation
			Euler’s Method
			Euler’s Method Practice
10	Sep 24	Euler’s Method (II)	Error
			Problems with Euler
			Variations of Euler
			Python Implementation
			dsolve app
11	Sep 26	Second-Order ODE	Second-Order ODE
			Factoring Method
			Distinct Roots Practice
			Repeated Roots
			Repeated Roots Practice
12	Sep 29	Complex Roots	Complex Numbers
			Complex Roots
			Complex Roots Practice
			Summary: 3 Cases
13	Oct 1	Boundary-Value Problems	Motivation
			Boundary-Value Problems
			Derivative Example
14	Oct 3	Undetermined Coefficients	Inhomogeneous Equations
			Undetermined Coeffs: Rule 1
			Undetermined Coeffs: Rule 2
			Undetermined Coeffs: Rule 3
			Sums of Terms
			Resonance
			Who’s that particular solution?
15	Oct 6	Mech and Forced Vibrations	Mass Spring Demo
			Mass Spring Derivation
			Free Vibrations
			Damping
			Forcing
			Resonance
16	Oct 8	Variation of Parameters (I)	Cramer’s Rule
		The Wronskian (optional)	The Wronskian
			Variation of Parameters
			Var of Par Derivation
			Var of Par Practice
17	Oct 10	Midterm 1 – Review	Integrating Factors
			Separation of Variables
			Exact Equations
			Second-Order ODE
			More Second-Order ODE
	Oct 15	Midterm 1
18	Oct 17	Variation of Parameters (II)
19	Oct 20	The Laplace Transform	Laplace Transform
			Laplace Transform Examples
			Tabular Integration
			Laplace Miracle
20	Oct 22	Applications to ODE	Applications to ODE
			Inhomogeneous Example
21	Oct 24	Step Functions (I)	Step Functions
			Simple Jumps
			General Jumps
			Jump Practice
			Reverse Way
22	Oct 27	Step Functions (II)	Shifting
			Reverse Way
			Summary: Four Cases
			Completing the Square
			Putting everything together
23	Oct 29	ODE with jumps	ODE with jumps
			ODE with shifts
24	Oct 31	Dirac Delta	Dirac and Roll
			Dirac Delta Construction
			Dirac Delta Laplace Transform
			ODE with Dirac Delta
			More Practice
25	Nov 3	Convolution	Convolution
			Convolution and ODE
			Integral Equations
			Integro-Differential Equation
			The Laplast One
26	Nov 5	Systems of ODE (I)	Systems of ODE
			Matrix Form
			Higher-Order ODE
27	Nov 7	Linear Algebra Review	Eigenvalues and Eigenvectors
		Full Version	How to find eigenvalues
			How to find eigenvectors
			Diagonalization
28	Nov 10	Systems of ODE (II)	Solving Systems of ODE
			Why this works
			Phase Portraits
			Initial Conditions
29	Nov 12	Complex Eigenvalues	Complex Eigenvalues
			Complex Eigenvalues Practice
			pplane app
30	Nov 14	Repeated Eigenvalues	Repeated Eigenvalues
		Peyamstagram	Why this works
			Peyamstagram
31	Nov 17	Midterm 2 – Review	Laplace Transforms
			Inverse Laplace Transforms
			Variation of Parameters
			Who’s that particular solution?
	Nov 19	Midterm 2
32	Nov 21	Variation of Parameters	Variation of Parameters
			Why this works
			More Practice
33	Nov 24	Nonlinear Systems	Nonlinear Systems
			Equilibrium Points
			Classification
34	Dec 1	Ecology: Competing Species	Competing Species
			Equilibrium Points
			Classification
			Conclusion
35	Dec 3	Epidemiology: COVID Model	COVID Model
			Re-scaling time
			COVID outbreaks
36	Dec 5	Exam 3 – Review	Nonlinear ODE
			Chemical Tanks
			Variation of Parameters
			Who’s that particular solution?
	Dec 12	Final Exam

Assignments

Homework	Due Date	Solutions
Homework 1	Sep 12	Solutions
Homework 2	Sep 19	Solutions
Homework 3	Sep 26	Solutions
Homework 4	Oct 3	Solutions
Coding 1	Oct 3	Solutions
Homework 5	Oct 10
Homework 6	Oct 24
Homework 7	Oct 31
Coding 2	Oct 31
Homework 8	Nov 7
Homework 9	Nov 14
Coding 3	Nov 14
Homework 10	Dec 5
Mini Project	Dec 5
Homework 11	Dec 12

YouTube Playlists

Chapter	Playlist
1	Introduction
2	First-Order ODE
3	Second-Order ODE
4	Laplace Transforms
5	Systems of ODE
6	Nonlinear ODE

Recitation Session Notes (courtesy Nadine Ansorge)

Recitation	Date	Solutions
Recitation 1	Sep 9	Solutions
Recitation 2	Sep 16	Solutions
Recitation 3	Sep 23	Solutions
Recitation 4	Sep 30	Solutions

Exams

Exam 1: Wednesday, October 15, covers Lectures 1-12

Practice Exam	Solutions	Comments
Study Guide
Mock Midterm 1	Solutions
Mock Midterm 2	Solutions	Spring 2022 Midterm 1
Mock Midterm 3	Solutions	Spring 2023 Midterm 1
Mock Midterm 4	Solutions	Summer 2023 Midterm 1
Mock Midterm 5	Solutions	Fall 2023 Midterm 1
Mock Midterm 6	Solutions	Spring 2024 Midterm 1
Mock Midterm 7	Solutions	Summer 2024 Midterm 1
Mock Midterm 8	Solutions	Fall 2024 Midterm 1
Mock Midterm 9	Solutions	Summer 2025 Midterm 1
Exam 1 – Review
More Exam 1 – Review		Courtesy Caleb Evert

Exam 2: Wednesday, November 19, covers Lectures 11-25

Practice Exam	Solutions	Comments
Study Guide
Laplace Table
Mock Midterm 1	Solutions
Mock Midterm 2	Solutions	Spring 2022 Midterm 2
Mock Midterm 3	Solutions	Spring 2023 Midterm 2
Mock Midterm 4	Solutions	Summer 2023 Midterm 2
Mock Midterm 5	Solutions	Fall 2023 Midterm 2
Mock Midterm 6	Solutions	Spring 2024 Midterm 2
Mock Midterm 7	Solutions	Summer 2024 Midterm 2
Mock Midterm 8	Solutions	Fall 2024 Midterm 2
Mock Midterm 9	Solutions	Summer 2025 Midterm 2
Exam 2 – Review

Exam 3: Friday, December 12, covers the entire course

Practice Exam	Solutions	Comments
Study Guide
Laplace Table
Mock Final 1	Solutions
Mock Final 2	Solutions	Spring 2022 Final
Mock Final 3	Solutions	Spring 2022 Final
Mock Final 4	Solutions	Fall 2022 Midterm
Mock Final 5	Solutions	Fall 2022 Final
Mock Final 6	Solutions	Spring 2023 Final
Mock Final 7	Solutions	Summer 2023 Final
Mock Final 8	Solutions	Fall 2023 Final
Mock Final 9	Solutions	Spring 2024 Final
Mock Final 10	Solutions	Summer 2024 Final
Mock Final 12	Solutions	Summer 2025 Final
Exam 3 – Review

Calendar